Diversity of interpretations of quantum mechanics is often considered as a sign of foundational crisis. In this note we proceed towards unification the relational quantum mechanics of Rovelli, Bohmian mechanics, and many worlds interpretation on the basis so called Dendrogramic Holographic Theory (DHT). DHT is based on the representation of observed events by dendrograms (finite trees) presenting observers subjective image of universe. Dendrograms encode the relational hierarchy between events, in applications they are generated by clustering algorithms; an algorithm with the branching index p >1 generate p-adic trees. The infinite p-adic tree represents the ontic event universe. We consider an ensemble of observers performing observations on each other and representing them by p-adic trees. In such “observers universe” we introduce a kind of Minkowski space structure, which is statistical by its nature. This model unites the observer/system discrepancy. Measurements are performed by observers on observers. Such “observers universe” is dynamically changing and is background independent since the space itself is emergent. And within this model, we unify the aforementioned interpretations.
Quantum mechanics (QM) is derived based on a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between events. All events are coupled through the tree structure. Such a holistic picture of event-processes was formalized within the Dendrographic Hologram Theory (DHT). The present paper is devoted to the emergence of QM from DHT. We used the generalization of the QM-emergence scheme developed by Smolin. Following this scheme, we did not quantize events but rather the differences between them and through analytic derivation arrived at Bohmian mechanics. We remark that, although Bohmian mechanics is not the main stream approach to quantum physics, it describes adequately all quantum experiments. Previously, we were able to embed the basic elements of general relativity (GR) into DHT, and now after Smolin-like quantization of DHT, we can take a step toward quantization of GR. Finally, we remark that DHT is nonlocal in the treelike geometry, but this nonlocality refers to relational nonlocality in the space of events and not Einstein's spatial nonlocality. By shifting from spatial nonlocality to relational we make Bohmian mechanics less exotic.
Abstract This is a brief review on the basics of recently established Dendrogramic Holographic theory (DH-theory). This is the special model of the event-universe based on the clustering transformation of experimental data into dendrogram, a finite tree which branches encoding the events. These event-branches are coupled via the hierarchic interrelation determined by the dendrogram. Such relational universe differs from the universe with space-time mathematically described by the real numbers. Dendrogram is endowed with the common root ultrametric. Finite dendrograms correspond to the epistemic level of description; in the limit we obtain an infinite tree providing the ontic description. In the simplest model, the tree is homogeneous, p-adic tree. It can be endowed with the algebraic structure of the ring of p-adic integers. Hence, DH-theory is a part (but very special) of p-adic theoretical physics. In this paper we discuss the foundations of DH-theory and its applications to quantum-classical interrelation including the novel interpretation of the violations of the CHSH-inequality, to general relativity, and to emergence of quantum mechanics from the event-picture of the universe. Since both quantum theory and general relativity can be emergent from DH-theory, creation of the latter can be viewed as a step towards unification of these two fundamental physical theories.
This paper is devoted to event-observational modelling in physics and more generally natural science. The basic entities of such modelling are events and where space-time is the secondary structure for the representation of events. The novelty of our approach is in using a new mathematical picture of events universe. The events observed by an observer are described by a dendrogram, a finite tree. The event dynamics are realized in the dendrogramic configuration space. In a dendrogram, all events are intercoupled via the hierarchic relational structure of the tree. This approach is called Dendrogramic Holographic Theory (DHT). We introduce the causal structure on the dendrogramic space, like the causal structure on the Minkowski space-time. In contrast to the latter, DHT-emergent causality is of a statistical nature. Each dendrogram represents an ensemble of observers with the same relational tree representation of the events they measured/collected. Technically the essence of causal modelling is in encoding dendrograms by real parameters and in this way transitioning to the real space-time. Then we proceed in the framework of information geometry corresponding to Hellinger distance and introduce a kind of light cone in the space of dendrograms. This is a step towards the development of DHT-analog special relativity.
Abstract Dendrogramic Holographic Theory (DHT) is a purely relational theory of information in which the primitive elements are events, and physical description is defined by an observer’s dendrogram: a hierarchical tree of binary questions that distinguishes events only through operationally accessible relations. The core postulate is an epistemic form of Leibniz’s Principle of the Identity of Indiscernibles: if two states of affairs cannot be distinguished by any admissible measurement for a given observer, they are identified for that observer. From each dendrogram we construct a views distribution over relational distances and define a one-particle wavefunction from that distribution; many distinct relational configurations can therefore map to the same distribution and the same wavefunction, so a particle is naturally an equivalence class of dendrograms sharing the same wavefunction. We then study two-particle sectors by embedding a pair of finite dendrograms into a host context consisting of one or two larger dendrograms, allowing both equal host and distinct-host comparisons and accommodating a range of size relations. When neither host can be embedded into the other, the host pair is space-like separated in a Minkowski-like parameter space, so exchange signatures arise purely from the relative organization of the embedded structures rather than from causal nesting. Our simulations show that bosonic versus fermionic exchange behaviour is not an intrinsic label of the embedded inputs, but an emergent invariant of the composite relational wiring diagram linking two, often non-relationally closed, information sets through cross-host correlations, reproducing exclusion-like and pile-up behaviour without postulating the Pauli principle. In this sense, DHT offers a unifying perspective on bosonic and fermionic fields: both arise from the same underlying relational degrees of freedom, and boson–fermion conversion corresponds to operations that break or restore relational closure, by changing host choice and embedding pattern, while leaving the one-particle state fixed—an analogue of supersymmetric unification that does not require a new particle spectrum. This suggests a unification of matter and forces at the level of relational organization without introducing new particles and while remaining compatible with a Minkowski-like spacetime encoding.
Dendrogramic Holographic Theory (DHT) is a purely relational theory of information in which the primitive elements are events, and physical description is defined by an observer’s dendrogram: a hierarchical tree of binary questions that distinguishes events only through operationally accessible relations. The core postulate is an epistemic form of Leibniz’s Principle of the Identity of Indiscernibles: if two states of affairs cannot be distinguished by any admissible measurement for a given observer, they are identified for that observer. From each dendrogram we construct a ``views distribution''
ρ over relational distances and define a one-particle wavefunction by
∣ψ∣2=ρ; many distinct relational configurations can therefore map to the same distribution and the same
ψ, so a ``particle'' is naturally an equivalence class of dendrograms sharing the same wavefunction. We then study two-particle sectors by embedding a pair of finite dendrograms
(TA,TB) into a host context consisting of one or two larger dendrograms
(HC,HD), allowing both equal-host and distinct-host comparisons and accommodating a range of size relations. When neither host can be embedded into the other, the host pair is space-like separated in a Minkowski-like parameter space, so exchange signatures arise purely from the relative organization of the embedded structures rather than from causal nesting. Our simulations show that bosonic versus fermionic exchange behaviour is not an intrinsic label of
TA or
TB, but an emergent invariant of the composite relational wiring diagram linking two (often non-relationally closed) information sets through cross-host correlations, reproducing exclusion-like and pile-up behaviour without postulating the Pauli principle. In this sense, DHT offers a unifying perspective on bosonic and fermionic fields: both arise from the same underlying relational degrees of freedom, and ``boson--fermion conversion'' corresponds to operations that break or restore relational closure (by changing host choice and embedding pattern) while leaving the one-particle state
ψ fixed---an analogue of supersymmetric unification that does not require a new particle spectrum. This suggests a unification of ``matter'' and ``forces'' at the level of relational organization without introducing new particles and while remaining compatible with a Minkowski-like spacetime encoding.
A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibniz principle of the Identity of Indiscernibles. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Conceptually, our theory is very close to Smolin’s dynamics of difference and Rovelli’s relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.